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单词 Cone
释义

cone


Given a topological spaceMathworldPlanetmath X, the cone on X (sometimes denoted by CX) is the quotient spaceMathworldPlanetmath X×[0,1]/X×{0}. Note that there is a natural inclusion XCX which sends x to (x,1).

If (X,x0) is a based topological spacePlanetmathPlanetmath, there is a similar reduced cone construction, given by X×[0,1]/(X×{0})({x0}×[0,1]). With this definition, the natural inclusion x(x,1) becomes a based map, where we take (x0,0) to be the basepoint of the reduced cone.

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更新时间:2025/5/4 12:01:12